Apparatus for generating biphasic waveforms in an implantable defibrillator

ABSTRACT

A method and apparatus for generating biphasic waveforms for an implantable defibrillator uses two disparate capacitor systems. A first phase of the biphasic waveform is generated from the charge stored in a first capacitor system, and a second phase of less energy than the first phase is generated from the charge stored in a second capacitor system. By using a second capacitor system for the second phase of the biphasic waveform that stores less energy than the first capacitor system, the overall size and power requirements of the implantable device can be reduced. In a preferred embodiment, the disparate capacitor systems have different effective capacitances, with the second capacitor system preferably having a higher effective capacitance, but a lower charging voltage, than the first capacitor system.

REFERENCE TO RELATED APPLICATION

This application is a continuation of application Ser. No. 132,634, filed 6 Oct. 1993, now abandoned.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates generally to implantable defibrillator systems, and more particularly, to a method and apparatus for generating biphasic waveforms with an implantable defibrillator system.

2. Background of the Invention

Implantable defibrillator systems deliver a high voltage electrical countershock to the heart in an attempt to correct or convert a detected cardiac arrhythmia or fibrillation. Due to the limitations on size and power imposed by the fact that these systems must be self-contained implantable devices, all existing implantable defibrillator systems generate an electrical countershock by charging a capacitor system to a high voltage. The electrical charge stored in the capacitor system is then delivered as a truncated capacitive discharge through two or more implanted electrodes.

To date, there have been two basic kinds of truncated capacitive discharge waveforms which have been used with implantable defibrillator systems: monophasic waveforms and biphasic waveforms. Monophasic waveforms are comprised of a single monotonically decaying electrical pulse that is typically truncated before the capacitor system is completely discharged. Biphasic waveforms, on the other hand, are comprised of a pair of decaying electrical pulses or phases that are of opposite polarity. To generate a biphasic pulse, a first pulse or phase is discharged from the capacitor system in the same manner as a monophasic waveform and then, at the point the first pulse is truncated, an H-bridge switch circuit connected to the electrodes is used to immediately reverse the discharge polarity of the capacitor system as seen by the electrodes in order to produce the second pulse or phase of the biphasic waveform that is of the opposite polarity. A typical example of the use of an H-bridge circuit to generate a biphasic waveform in an implantable defibrillator system is shown in U.S. Pat. No. 4,998,531.

Over the last twenty five years, it has been demonstrated that appropriately truncated biphasic waveforms can achieve defibrillation with significantly lower currents, voltages and energies than monophasic waveforms of similar durations. Kroll, M W et al., "Decline in Defibrillation Thresholds", PACE 1993; 16#1:213-217; Bardy, G H et al., "A Prospective Randomized Evaluation of Biphasic vs. Monophasic Waveform Pulses on Defibrillation Efficiency in Humans", J American College of Cardiology, 1989; 14:728-733; and Wyse, D G et al., "Comparison of Biphasic and Monophasic Shocks for Defibrillation using a Non-Thoracotomy System", American J Cardiology 1993; 71:197-202. These findings are of particular importance for implantable devices because of the direct relationship between the amount of energy required for defibrillation and the overall size of the implantable device, i.e., the lower the energy required for defibrillation, the smaller the device.

Numerous theories have been advanced to explain the improved efficiency of the biphasic waveform over the more conventional monophasic waveform. Although some of these theories may partly explain, or may act cooperatively to explain, the effect that a biphasic waveform has on the heart, there is currently no single accepted theory which fully explains the advantages of the biphasic waveform over the monophasic waveform. As a result, there is little or no agreement on what factors might further improve the efficiency and operation of the biphasic waveform.

In terms of the circuity used to generate biphasic waveforms, the conventional H-bridge switch circuit has proven to be the only circuit used to generate biphasic waveforms in existing manufactured implantable cardioverter defibrillator (ICD) systems. Unfortunately, the switching components required for the conventional H-bridge circuit have two drawbacks. First, there is some question as to the long-term reliability of the switching components when used for this application. Second, the switching components are relatively large and their use tends to decrease the space in the ICD system that would otherwise be available for batteries or capacitors. In addition, the use of the conventional H-bridge circuit require a capacitor system that will have sufficient residual charge after truncation of the first phase to adequately power the second phase of the biphasic pulse. With existing ICD systems, all of which have capacitor systems with effective capacitance values of 140 μf or greater, this has not been a problem. As ICD systems are developed with smaller capacitance values, however, the amount of residual charge left in the capacitor system may not be sufficient to adequately power the second phase of the biphasic pulse.

The only other circuit design that has been proposed for generating biphasic waveforms arose out of the early theory that biphasic countershocks were more efficient because the net electrical charge transport was zero for a perfectly symmetrical biphasic waveform were the second phase was an exact mirror of the first phase. Schuder, J C et al. "Transthoracic Ventricular Defibrillation with Square-Wave Stimuli: One-Half Cycle, One Cycle and MultiCycle Waveforms", Circulation Research, 1964; 15:258-264. In recent experiments testing this theory, two capacitors were used to generate a "double capacitor" biphasic waveform in which a separate capacitor was used for each phase of a symmetric biphasic waveform to ensure complete symmetry of the waveform. The results of these experiments established that dual capacitor systems were inferior to single capacitor system in terms of producing lower defibrillation threshold energies for symmetric biphasic waveforms. Kavanagh, K M et al., "Comparison of the Internal Defibrillation Thresholds for Monophasic and Double and Single Capacitor Biphasic Waveforms", J American College of Cardiology, 1989; 14:1343-1349; and Freeser, S A et al., "Strength-Duration and Probability of Success Curves for Defibrillation with Biphasic Waveforms", Circulation, 1990; 82:2128-2141.

While existing implantable defibrillator systems are capable of generating electrical countershocks that utilize the more efficient biphasic waveform, there presently is no single accepted theory for why the biphasic waveform is more efficient. This lack of an understanding of the nature and effect of the biphasic waveform has impeded further development and enhancement of the biphasic waveform. Accordingly, it would be desirable to provide a method and apparatus for generating biphasic waveforms for an implantable defibrillator system that overcomes the disadvantages of the existing H-bridge circuitry. It would also be advantageous to improve on the methods and apparatus for generating biphasic waveforms as a result of an improved understanding of the nature and effect of the biphasic waveform on the fibrillating myocardium.

SUMMARY OF THE INVENTION

The present invention provides a method and apparatus for generating biphasic waveforms for an implantable defibrillator using two disparate capacitor systems. A first phase of the biphasic waveform is generated from the charge stored in a first capacitor system, and a second phase of less energy than the first phase is generated from the charge stored in a second capacitor system. By using a second capacitor system for the second phase of the biphasic waveform that stores less energy than the first capacitor system, the overall size and power requirements of the implantable device can be reduced. In a preferred embodiment, the disparate capacitor systems have different effective capacitances, with the second capacitor system preferably having a higher effective capacitance, but a lower charging voltage, than the first capacitor system.

Many theories have been offered for the improved efficacy of the biphasic defibrillation waveform. The present invention uses a unique quantitative model based on the theory that the function of the first phase of the biphasic waveform is to synchronize the myocardium as is done with a conventional monophasic wave, and the function of the second phase is to remove any residual charge from the cell membranes, which was deposited by the first phase of the shock. The model used by the present invention assumes that the effective current requirement of the first phase are a linear function of the calculated residual (after the second phase) cell membrane voltage squared. For an ICD system having a single capacitor system, the model utilized by the present invention predicts that the duration of the second phase should be a constant of about 2.5 ms for the range of presently encountered ICD capacitances and electrode resistances.

The present invention uses this model to optimize the generation of biphasic waveforms for an implantable defibrillator having two disparate capacitor systems.

BRIEF DESCRIPTION OF THE DRAWING

FIG. 1 shows the output voltages for a typical biphasic waveform produced by a single capacitor system implantable defibrillator.

FIG. 2 is a schematic diagram of the circuitry in existing ICD systems that is used to produce the biphasic waveform as shown in FIG. 1.

FIG. 3 is a simplified schematic diagram of the ICD system shown in FIG. 2 and including an electrical cell model of the heart.

FIG. 4 is a further simplified schematic diagram of the ICD system shown in FIG. 3.

FIG. 5 is a graph of the electrode and membrane voltages for a 5/5 ms biphasic waveform from a 2000 μF capacitor and 50 Ω electrode resistance that approximates a symmetric biphasic waveform.

FIG. 6 is a graph of the optimum duration of the first and second phases of a single capacitor system biphasic waveform as a function of the RC time constant as derived by the biphasic model of the present invention.

FIG. 7 is a graphs of the phase 2 duration as a percentage of the duration of phase 1 for optimal thresholds of a single capacitor system biphasic waveform according to the present model.

FIG. 8 is a graph of optimum tilts for phases 1 and 2 as a function of RC time constant for a single capacitor system according to present model.

FIG. 9 is a schematic diagram of the disparate capacitor system circuitry of the present invention for producing a biphasic waveform.

FIG. 10 shows the output voltages of a first biphasic waveform produced by the disparate capacitor system of the present invention in which the charging voltages of the disparate capacitors are identical.

FIG. 11 shows the output voltages of a second biphasic waveform produced by the disparate capacitor system of the present invention in which the charging voltages of the disparate capacitors are different.

FIGS. 12-15 shows the output voltages of various alternative embodiments of the second biphasic waveform as shown in FIG. 11.

FIG. 16 shows the output voltage for a typical biphasic waveform produced by a single capacitor system implantable defibrillator.

FIGS. 17-18 show the output voltage for a biphasic waveform similar to that of FIG. 16, but produced by the disparate capacitor system of the present invention.

FIGS. 19-22 are more detailed schematic diagrams of alternate embodiments of the disparate capacitor system circuitry of the present invention for producing a biphasic waveform.

DESCRIPTION OF THE PREFERRED EMBODIMENT

The description of the preferred embodiment will first review the standard biphasic waveform and single capacitor system circuitry which is used to produce that waveform in existing ICD systems. With this background in mind, a review of the present biphasic theories, as well as the results of known experimental data on biphasic waveforms and defibrillation, is presented. Next, a new model for understanding biphasic waveforms is presented. The new model is first applied to optimize biphasic waveforms produced by single capacitor system. Finally, the new model is used to support the advantages of the disparate dual capacitor system of the preferred embodiment of the present invention.

Existing ICD Systems and Biphasic Waveforms

FIG. 1 shows the output voltages of an electrical countershock for a typical biphasic waveform 10 produced by a single capacitor system implantable defibrillator. Biphasic waveform 10 consists of a first phase 12 shown as having a positive polarity and a second phase 14 shown as having a negative polarity, although it will be understood that the polarities of the phases 12 and 14 could be reversed, so long as the respective polarities of phases 12 an 14 are opposite one another. In addition to the electrode voltage for biphasic waveform 10, FIG. 1 also shows a typical myocardial cell membrane voltage 16 in response to the delivery of the electrical countershock. For ease of representation, the voltages shown in FIG. 1 are shown as normalized voltages expressed in arbitrary percentage units of the initial charging voltage 18 of the single capacitor system.

FIG. 2 shows a schematic diagram of the circuitry 20 that is used in existing implantable cardioverter defibrillator (ICD) systems to produce biphasic waveform 10 as shown in FIG. 1. Battery system 22 activates a primary winding on flyback split winding transformer 24 when switch 26 is activated by controller 28. Each of the split secondary windings of transformer 24 charges capacitor system 30, consisting of a pair of electrolytic capacitors 30a or 30b, through diode 32a or 32b, respectively. Switches 34, 35, 36 and 37 are connected in a conventional H-bridge switch arrangement as shown to electrodes 40 and 42 to deliver biphasic waveform 10 to the heart 44. During delivery of first phase 12, switches 34 and 37 are closed and switches 35 and 36 are open. At the transition point at the end of first phase 12 and the beginning of second phase 14, controller 28 opens switches 34 and 37 and closes switches 35 and 36 to reverse the polarity and current flow of the countershock delivered through electrodes 40 and 42, thereby producing biphasic waveform 10. An example of circuitry 20 is shown and described in further detail in U.S. Pat. No. 4,998,531.

It will be seen that by charging and discharging capacitors 30a and 30b in series, the effectiveness capacitance of capacitor system 30 is the series combination of the individual capacitance values of capacitors 30a and 30b, i.e., one-half of each of the individual capacitance values, while the discharge voltage can be twice the maximum charging voltage of the individuals capacitors 30a or 30b. In this way, electrolytic capacitors which have a relatively higher energy density, but which have a maximum charging voltage of only about 375 volts, can be used in an ICD system that need to generate defibrillation countershocks having discharge voltages of at least 500 volts.

Present Biphasic Theories

Many theories have been proposed to explain the improved efficacy of the biphasic waveform. Several of these may be relevant and may in fact act jointly. To date, the following general theories have been advanced in the literature: (1) zero net charge transfer; (2) current summing; (3) sodium channel reactivation; (4) shortening of the refractory period; (5) lowering of the impedance; (6) improved energy delivery; and (7) change in the critical point. Each of these theories will be briefly summarized to contrast them with the theory employed by the present invention.

(1) Zero Net Charge Transfer--The first paper on the biphasic defibrillation waveform was arguably presented by Schuder in 1964. In that paper he observed, "an important feature of the one-cycle bi-directional shock is that, despite the arbitrary starting point, the net electrical charge transport is zero." Schuder J C, Stoeckle E H, Dolan A M, "Transthoracic Ventricular Defibrillation with Square-Wave Stimuli: One-Half Cycle, One Cycle, and MultiCycle Waveforms", Circulation Research 1964;15:258-264. However, a recent study found a negative correlation between the charge contents in each phase of efficient biphasic shocks of a certain design. Walker R G, Walcott G P, Swanson D K, et.al., "Relationship of Charge Distribution between Phases in Biphasic Waveforms", Circulation 1992;86 No.4:I-792. (Abstract). This would imply that a zero net charge transfer was not required or necessarily efficient, and that a zero net charge transfer (at least at the electrode level) may not be important for the efficacy of a biphasic waveform.

(2) Current Summing--It has also been suggested that when the second phase of a biphasic pulse is removed, thereby creating a monophasic pulse, it is necessary to increase the discharge voltage of this pulse so that the current amplitude would be equal to the sum of current values of 2 first half periods for the discharge. Consequently, the capacity of the heart to summate the stimulation effect of both phases of current may be utilized for reduction of the defibrillating current in one direction and for decreasing the hazard of the heart injury by a strong current. Gurvish N L, Markarychev, V A: "Defibrillation of the Heart with Biphasic Electrical Impulses", Kardiologilia 1967;7:109-112. A similar result was found more recently suggesting that the total voltage change from the trailing edge of the first phase to the leading edge of the second phase was an important factor in the defibrillation pulse. Tchou P, Krum D, Aktar M, Avitall B, "Reduction of Defibrillation Energy Requirements with new Biphasic Waveforms", PACE 1990; 13:507. (Abstract) The summing hypothesis is tempting in that the sum of the currents (or voltages) in the two phases of a biphasic shock is indeed comparable to the current in a monophasic shock of similar efficacy. However, this theory does not explain the sensitivity of the biphasic efficiency to the duration of the second phase.

(3) Reactivation of the Sodium Channels--It has been suggested that the first phase of the biphasic waveform serves as a conditioning prepulse which helps to restore sodium channel activation in preparation for the excitation by the second phase. Jones J L, Jones R E, Balasky G, "Improved Cardiac Cell Excitation with Symmetrical Biphasic Defibrillator Waveforms", American J Physiology 1987;253:H1418-H1424. This reactivation hypothesis was given additional support and a theoretical underpinning in a later paper which demonstrated that a hyperpolarizing prepulse did reactivate additional sodium channels thus promoting increased excitability. Kavanagh K M, Duff H J, Clark R, et.al., "Monophasic vs. Biphasic Cardiac Stimulation: Mechanism of Decreased Energy Requirements", PACE 1990:13;1268-1276. This theory may explain why the biphasic wave prolong refractoriness after the shock. Swartz J F, Jones J L, Jones R E, Fletcher R D, "Conditioning Prepulse of Biphasic Defibrillator Waveforms Enhances Refractoriness to Fibrillation Wavefronts", Circulation Research 1991;68:438-449. Unfortunately, this enhanced stimulation effect is very dependent on waveform duration. Karasik P, Jones R, Jones J., "Effect of Waveform Duration on Refractory Period Extension Produced by Monophasic and Biphasic Defibrillator Waveforms", PACE 1991;14:715. (Abstract). Thus, the reactivation theory for biphasic waveforms may or may not be important depending upon the importance of the extension of refractory period vs. synchronization as the fundamental basis of defibrillation.

(4) First Phase Shortening of Refractory Period--It has been long known that a hyperpolarizing pulse delivered during phase 2 of the action potential can shorten the refractory period, thus, allowing a depolarizing pulse to more easily activate the cell, and it has been suggested that this mechanism could explain the increased effectiveness of the biphasic shock. Tang A S L, Yabe S, Wharton J M, et.al., "Ventricular Defibrillation Using Biphasic Waveforms: The Importance of Phasic Defibrillation", J American College of Cardiology 1989;13:207-14. This proposed theory is similar to the sodium channel reactivation hypothesis and the cited literature may apply in both cases.

(5) Lower Impedance--There is some evidence that the average current of a pulse is the best measure of its effectiveness (for a given pulse duration). Bourland J D, Tacker W A, Geddes L A. et al., "Comparative Efficacy of Damped Sign Wave and Square Wave Current for Transchest Ventricular Defibrillation in Animals", Medical Instrumentation 1978;12#1:38-1. Thus, for a given voltage in a waveform, one would expect that the waveform with the lowest impedance would be the most efficacious. It has been found that the average impedance of the second phase of a biphasic waveform is significantly lower than that of the first phase. Tang A S L, Yabe S, Wharton J M, et.al., "Ventricular Defibrillation Using Biphasic Waveforms: The Importance of Phasic Defibrillation", J American College of Cardiology 1989;13:207-14. The lower impedance theory, however, is suspect for two reasons. First, the reductions in required voltage are found to be lower than the impedance reductions and, as a result, the current requirement is itself reduced for the biphasic waveform. Second, the impedance reduction results from the transition between the phases and thus only benefits the second phase of the shock. As a result, the lower impedance theory does not explain the overall improvements in efficacy which have been observed for the biphasic waveform.

(6) Improved Energy Delivery--It has been suggested that the increased efficacy of the biphasic waveform is due to its ability to deliver a larger fraction of the energy in the capacitor for a typical capacitive discharge defibrillator. U.S. Pat. No. 4,850,357, issued to Bach and entitled "Biphasic Pulse Generator for an Implantable Defibrillator". Clearly one could deliver more of the energy in a capacitor by merely increasing the duration of the pulse, but this has been shown to be deleterious in that long durations can lower the average current and thereby decrease efficiency. Kroll M W, Adams T P, "The Optimum Pulse Width for the Implantable Defibrillator", 7th Purdue Conference on Defibrillation, American Heart Journal 1992;124#3:835. (Abstract).

For general stimulation and defibrillation, it has been shown that pulses significantly wider than the appropriate chronaxie time use energy inefficiently. Irnich W, "The Chronaxie Time and its Practical Importance", PACE 1980;8:870-888. By delivering the energy in two shorter phases, one could utilize the energy without the penalty of the increased duration. A reasonably efficient capacitive discharge monophasic waveform will deliver nearly 90% of the capacitor's energy with an efficient pulse duration. By use of the biphasic waveform one can thus deliver another 10% of the energy. However the energy reductions reported, for biphasic usage, are significantly greater than 10%. It has also been shown that, for a more optimal duration, the stored energy requirements were also lowered with the biphasic waveform. Swartz J F, Karasik P E, Donofrio J, et.al., "Effect of Biphasic Waveform Tilt on Human Non-Thoracotomy Defibrillation Threshold", PACE 1993;16#4II:888 (Abstract). Thus, the argument that the increased benefit of biphasic waveforms might lie from increasing the percentage of energy delivered can certainly not account for all of the effects which have been observed.

(7) Differences in the Critical Point--It has been suggested that differences in the critical point of the biphasic waveform may explain its advantage over the monophasic waveform. Ideker R E, Tang A S L, Frazier D W, et.al., "Ventricular Defibrillation: Basic Concepts", Cardiac Pacing and Electrophysiology 3rd Ed., edited by El-Sherif N & Samatt, W B Saunders Co. Philadelphia 1991;42:713-726. Re-entry may be induced when a sufficient potential gradient exists that is at an angle (e.g., perpendicular) to the dispersion of refractoriness. This has been shown to exist with a shock field of 5 V/cm in tissue just recovering from its effective refractory period. Frazier D W, Wolf P D, Wharton J M, et.al., "A Stimulus Induced Critical Point: A Mechanism for Electrical Initiation of Re-Entry in Normal Canine Myocardium", J of Clinical Investigation 1989;83:1039. According to this theory, it is thought, because these potential gradients exceeding the critical value can cause unidirectional block and prolongation of refractoriness, there is a lower critical point. If the biphasic shock has a lower critical point, then there is less of a chance of refibrillation from the shock. It has been shown, however, that the first reactivation following an unsuccesful countershock is typically found in the region with the lowest gradient, not the highest. Shibata N, Chen P S, Dixon E G, et. al., "Epicardial Activation After Unsuccessful Defibrillation Shocks in Dogs", American J Physiology 1988;255:H902-H909

Specific Experimental Findings on Biphasic Waveforms

Beside the experimental findings that the biphasic waveform has lower defibrillation thresholds, there are several specific findings which should be considered to better understand the nature of the difference between monophasic and biphasic waveforms. Most importantly, these experimental findings should be explainable by any putative theory of the biphasic waveform advantage. These specific findings are: (1) the biphasic wave generates fewer post shock arrhythmias; (2) a symmetric biphasic offers minimal or no benefit; (3) the second phase duration for a single capacitor shock should be shorter than the first duration; and (4) there is less benefit with the biphasic waveform for transthoracic defibrillation.

(1) Biphasic Waveform has Fewer Post Shock Arrhythmias--There are several reports that the biphasic waveform has fewer post shock arrhythmias than does the monophasic waveform for shocks of equal strength. This is certainly true for shocks near their threshold levels. This was first noted as a "distinct impression" without a statistical analysis in the early Schuder paper, and was confirmed in a recent study with dogs. Zhou X, Daubert J P, Wolf P D, et al., "Epicardial Mapping of Ventricular Defibrillation With Monophasic and Biphasic Shocks in Dogs", Circulation Research 1993;72:145-160. When the duration of the post shock arrhythmias is measured by detecting the contraction arrest time, it has been shown that the arrest time for rectangular biphasic waveforms with optimal durations could be reduced to half of the arrest time associated with monophasic waveforms of similar strength. Jones J L, Jones R E. Decreased Defibrillator--Induced Dysfunction with Biphasic Rectangular Waveforms. American J Physiology 1984;247:H792-H796.

(2) Symmetric Biphasic Offer Little or No Benefit--A study of isolated perfused canine hearts using symmetrical biphasic pulses--each phase had an identical amplitude and durations of 5 ms--showed no advantage in the threshold energy for defibrillation. Niebauer M J, Babbs C F, Geddes L A, et.al., "Efficacy and Safety of the Reciprocal Pulse Defibrillator Current Waveform", Medical and Biological Engineering and Computing 1984;22:28-31. In this study, myocardial depression was defined as the percentage decrease in systolic pressure, and it was found that the symmetric biphasic waveform also offered no advantage in minimizing myocardial depression at any multiple of the defibrillation threshold current.

As previously discussed in the background section, similar results were obtained with a "double capacitor" biphasic waveform in which a separate capacitor was used for each phase to ensure symmetry. Kavanagh K M, Tang A S L, Rollins D L, et.al., "Comparison of the Internal Defibrillation Thresholds for Monophasic and Double and Single Capacitor Biphasic Waveforms", J American College of Cardiology1989;14:1343-1349. Another example that symmetric biphasic waveforms offer no advantage is a study that used a single capacitor waveform of 7 ms which had a threshold of 1.19 J, while the symmetric dual capacitor waveform with both the first and second phase each being 7 ms had a 1.99 J threshold. Feeser S A, Tang A S L, Kavanagh K M, et.al. Strength--Duration and Probability of Success Curves for Defibrillation with Biphasic Waveforms. Circulation 1990;82:2128-2141.

(3) Efficient Biphasic Has Phase 2 Shorter than Phase 1--In a study done with a right ventricular catheter and a subcutaneous patch in dogs, single capacitor biphasic waveforms for which the first phase was 50, 75, and 90% of the total duration had a lower defibrillation energy threshold than a monophasic waveform of the same total duration. However for waveforms in which the second phase had 75 or 90% of the total duration the energy requirements increased significantly. Chapman P D, Vetter J W, Souza J J, et.al. "Comparative Efficacy of Monophasic and Biphasic Truncated Exponential Shocks for Nonthoracotomy Internal Defibrillation in Dogs. J American College of Cardiology 1988;12:739-745.

Similar results were found in dogs with epicardial patch electrodes in which a total of 25 combinations of first and second phase durations were studied. In all cases in which the second phase duration was shorter than the first phase duration, the total energy required was lower than that of a monophasic wave whose duration was equal to the first phase duration of the biphasic wave. Conversely, in all cases in which the second phase duration was greater than the first phase, the energy requirements were increased over the comparable monophasic waveform. Feeser S A, Tang A S L, Kavanagh K M, et.al., "Strength--Duration and Probability of Success Curves for Defibrillation with Biphasic Waveforms", Circulation 1990;82:2128-2141.

Still another canine study used both epicardial and pericardial patches found that the single capacitor biphasic waveforms with the lowest energy thresholds had a second phase shorter than the first phase. As with the other studies, those shocks with the second phase longer than the first phase had thresholds greater than that of comparable monophasic waveforms. Dixon E F, Tangas L, Wolf P D, Meador J T, Fine M G, Calfee R V, Ideker R E, "Improved Defibrillation Thresholds with Large Contoured Epicardial Electrodes and Biphasic Waveforms", Circulation, 1987;76:1176-1184.

(4) Biphasic Waveform Has Less Transthoracic Advantage--Another canine study compared monophasic and biphasic thresholds for both internal and external defibrillations. While the biphasic waveforms had energy thresholds that were approximately one half of those of the monophasic waveforms for internal defibrillation, the advantages of the biphasic waveform in external defibrillation, although still seen although, were usually not statistically significant when comparing waveforms of similar durations. Johnson E E, Hagler J A, Alferness C A, et al., "Efficacy of Monophasic and Biphasic Truncated Exponential Shocks for Nonthoracotomy Internal Defibrillation in Dogs", J American College of Cardiology, 1988;12:739-745.

Defibrillation at the Celluar and Tissue Level

Before describing the model for biphasic waveforms which is proposed and utilized by the present invention, it is important to review the present understanding of defibrillation at the cellular and tissue level. While defibrillation is presently understood fairly well at the celluar and tissue level for monophasic waveforms, as indicated by the numerous theories purporting to explain the efficacy of biphasic waveforms, there is no general understanding at the celluar and tissue level for biphasic waveforms.

Monophasic Waveform at the Cellular and Tissue Level--There is now strong evidence, from optical recordings, that the monophasic shock defibrillates by resynchronizing a large majority (i.e., at least 90%) of the myocardial cells. Dillon S M, "Synchronized Depolarization after Defibrillation Shocks: A Possible Component of the Defibrillation Process Demonstrated by Optical Recordings in Rabbit Heart", Circulation 1992;85:1865-1878. The requirement that a monophasic countershock resynchronize the large majority of myocardial cells is apparently due to the fact that a defibrillation strength shock will not only stimulate recovered cells (i.e. those in phase 4 or electrical diastole), but will also extend the activation potential of those already activated cells. This has been supported by non optical measurements showing that monophasic defibrillation shocks are indeed capable of extending the refractory period of activated cells in dogs, Sweeney R J, Gill R M, Steinberg M I, et.al., "Ventricular Refractory Period Extension Caused by Defibrillation Shocks", Circulation 1990;82:965-972; and humans, Belz M K, Speery R E, Wood M A, Ellenbogen K A, Stambler B S, "Successful Defibrillation Prolongs Action Potential Durations in Humans", PACE 993;16:932 (Abstract).

These results have created two semantic problems. First, it is now clear that the "absolute refractory" period is not absolutely refractory. It merely requires defibrillation strength shocks for stimulation. The second problem lies with the use of the word "stimulation". Stimulation has been traditionally used (in the narrow sense) as referring to electrical initiation of a new activation potential by opening the voltage gated sodium channels. While it appears that the activation potential prolongation is indeed initiated by the reopening of the sodium channels, this is not characteristic of conventional pacing stimulation, for example. To minimize confusion, the present invention will use the term "countershock stimulation" in reference to cell stimulation in a defibrillation context.

The difference between convention pacing stimulation and countershock stimulation may help to partially explain the nature of the defibrillation process. For example, the chronaxie time for far-field stimulation (in the conventional pacing sense) is on the order of 1 ms. Frazier D W, Krassowska W et al., "Extracellular Field Required for Excitation in Three-Dimensional Anisotropic Canine Myocardium.", Circulation Research 1988;63:147-164. The chronaxie time for the monophasic defibrillation pulse, on the other hand, has been consistently found to be in a range of 2-4 ms. Wessale J L, Bourland J D, Tacker W A, et al, "Bipolar catheter defibrillation in dogs using trapezoidal waveforms of various tilts", J Electrocardiology 1980; 13 (4):359-366; Niebauer M J, Babbs C F, Geddes L A, et al, "Efficacy and safety of defibrillation with rectangular waves of 2 to 20-milliseconds duration",Crit. Care Medicine 1983; 11 #2:95-98. A critical part of the defibrillation synchronization may be the countershock stimulation occurring in the refractory period. The increased difficulty of countershock stimulation in the so-called absolute refractory period may explain why the chronaxie time is increased from around 1 ms for pacing stimulation to around 3 ms for countershock stimulation.

Biphasic Waveform at the Cellular and Tissue Level--The exact mechanisms of biphasic defibrillation are not generally understood. Several qualitative findings exist, however, that, when properly interpreted, may give guidance towards an understanding of its mechanisms. These are that the biphasic waveform: (1) is an inferior stimulator compared to the monophasic waveform; (2) has less of a refractory period prolongation; and (3) has less post shock arrhythmias.

Biphasic is an Inferior Stimulator--Animal studies have compared the stimulation biphasic waveforms to that of monophasic waveforms and found that a biphasic pacing waveform required increased stimulus currents in relative refractory tissue, Wharton J M, Richard V j, Murry C E, et.al. "Electrophysiological Effects In Vivo of Monophasic and Biphasic Stimuli in Normal and Infarcted Dogs", PACE 1990;13:1158-1172; and that a biphasic defibrillation waveform was less effective in countershock stimulating partially refractory myocardium. Daubert J P, Frazier D W, Wolf P D, et.al. "Response of Relatively Refractory Canine Myocardium to Monophasic and Biphasic Shocks", Circulation 1991;84:2522-2538.

Biphasic has Smaller Refractory Period--Another animal study measured the activation potential prolongation from a shock delivered at a 50% repolarization point. A symmetric biphasic waveform was compared to monophasic waveforms. The biphasic waveform was able to generate a significantly smaller action potential prolongation for equal voltage shocks. Zhou X, Knisley S B, Wolf P D, et.al., "Prolongation of Repolarization Time by Electric Field Stimulation with Monophasic and Biphasic Shocks, in Open Chest Dogs", Circulation Research 1991;68:1761-1767.

Biphasic has Fewer Post Shock Arrhythmias--It has been already mentioned that the biphasic waveform generates less post shock arrhythmias. It has also been shown that the conduction block is less severe for the biphasic wave versus the monophasic wave and, for equal strength shocks, persists for less time. Yabe S, Smith W M, Daubert J P, et.al., "Conduction Disturbances Caused by High Current Density Electric Fields", Circulation Research 1990;66:1190-1203.

New Model For Biphasic Waveforms

Even with all of this information assembled, there is still no clear explanation for why the biphasic waveform is more efficient that the monophasic waveform. Consequently, there is no clear guidance on how, or even if, improvements can be made to the generation and delivery of biphasic waveforms. The present invention offers a model for the biphasic waveforms that appears to explain why the disparate dual capacitor system delivery of a biphasic waveform in accordance with the present invention is more efficacious than the existing technique of delivering biphasic waveforms from a single capacitor system.

The gist of the model that is utilized by the present invention is that the second phase of the biphasic waveform (when optimally sized) serves to remove the excess charge remaining on the cell membrane from the first phase. It is hypothesized that the excess charge remaining on cells after the countershock stimulation may end up creating a new arrhythmia some time after the countershock stimulation. Consequently, for a a monophasic shock to be successful, it must not only capture enough cells to halt fibrillation, but it must also capture enough cells so that no post shock arrhythmias as a result of the excess charge remaining on the cell membrane will occur. In other words, by having the second phase of a biphasic countershock return the cell membrane potentials to their pre-shock potential, there are fewer post shock arrhythmias, and, because there are fewer post shock arrhythmias, fewer cells need to be synchronized by the first phase. In addition, the protective refractory period extension requirement may be reduced. It is theorized that these two factors may explain the reduced amplitude requirements for the first phase.

The circuit model of the cell that is implicit in this discussion is essentially the standard capacitive membrane coupled to resistive paths giving a membrane time constant. Fozzard H A, "Membrane Capacity of the Cardiac Purkinje Fiber", J Physiol (Great Britain) 1966;182:255-267. In this model, V_(e) represents the voltage across the defibrillation electrodes and V_(m) represents the voltage across the membrane. The exact values of the resistances and capacitance are not important, the salient feature is the resulting membrane time constant which will be called τ_(m).

Referring again to FIG. 1, the voltages are shown as a function of time which would be expected in such a model for a biphasic waveform delivered from an existing ICD system having a single capacitor system. Assuming an ICD capacitance of 150 μF and an electrode resistance of 50 Ω, the electrode voltages will be as shown for a biphasic wave, with each phase having a duration of 3.5 ms. For ease of notation, the remaining discussion will refer to the duration of the a biphasic waveform in a shorthand form as "3.5/3.5", indicating that the first phase is 3.5 ms and the second phase is 3.5 ms. The capacitor voltages 12 and 14 for the first and second phases of the waveform 10 are shown beginning at a normalized value of 1.00 volts at 18. The membrane voltages 16 are calculated with the use of a representative time constant of the non-Purkinje ventricular cell membrane of approximately 3 ms. Weidmann S, "Electrical Constants of Trabecular Muscle from Mammalian Heart", J Physiol (Great Britain) 1970; 210: 1041-1054.

The exact transmembrane potential of an individual cell as shown in FIG. 1 is not relevant for this analysis. What is important is the perturbation, by the first phase 12 of the defibrillation countershock, of the membrane voltage 16 from its existing value. The model of the biphasic waveform utilized by the present invention suggests that the cancellation of this perturbation, i.e. the "burping" of the membrane charge, appears to be the critical function of the second phase. As can be seen from FIG. 1, at the end of the second phase, the transmembrane potential has been left, in this case, with a negative perturbation potential 19 as a result of the delivery of the biphasic waveform, instead of the desired zero perturbation potential which is the goal of the theory of the present invention.

The membrane voltage V_(m) is calculated as a fraction of the maximum potential attainable for an infinitely long rectangular pulse at the electrodes. The absolute value of the potential (in volts) is not critical as the return to zero is the sole goal of the biphasic waveform in accordance with the theory of the present invention. During the defibrillation shock the electric field will charge areas of the cell membrane positively, some negatively, and some not at all. Knisley S B, Blitchington T F, Hill B C, "Optical Measurement of Transmembrane Potential Changes During Electric Field Stimulation of Ventricular Cells",Circulation Research 1993;72:255-270. Also, depending upon the location of the cells vis-a-vis the electrodes, the actual membrane voltage will vary significantly. Using a normalized value (i.e. a fraction) for V_(m) allows the model to concentrate on the simple goal of returning the membrane voltage to a zero perturbation.

A quantitative model for the present invention can be determined with reference to FIGS. 3 and 4 which are schematic diagrams of an existing ICD system, of the type shown in FIG. 2, but coupled to a schematic lumped model of the electrical characteristics of the myocardial cells. FIG. 3 shows a circuit model of ICD system 20 and a representative myocyte cell of heart 44. ICD system 20 includes a main energy storage capacitor system 30 having an effective capacitance "C." To the right is the conventional H-bridge circuit with switch 34, 35, 36 and 37 for inverting the current flow for the two phases of the biphasic waveform. "R_(e) " is the inter-electrode resistance as shown at 46. Further to the right is a combination of a series resistor 50, a shunt resistor 52, and a membrane capacitance 54 for the analysis of the response of a representative cell to the defibrillation currents. The exact values of the resistances and capacitance are not important. The relative contribution to the time constant of the series resistances and the shunt resistances (from the so called leaky-capacitor model) is also not important. The salient feature is the resulting membrane time constant which will be called τ_(m). V_(e) represents the voltage across the defibrillation electrodes 42 and 44 and V_(m) represents the voltage across the membrane 44.

Consider the simplified schematic of FIG. 4 for analyzing the first phase of a biphasic countershock, or all of a monophasic shock. In FIG. 4, the H-bridge circuit of FIG. 3 is temporarily ignored and the resistance 52 in parallel with the membrane capacitance 54 is eliminated in favor of simplicity. This parallel (leaky membrane) resistance 52 may be ignored if R_(m) is taken as the Thevenin equivalent of the two resistors 50 and 52. Thus, R_(m) and C_(m) are the membrane series resistance and capacitance respectively. As before, the node V_(e) represents the voltage between the electrodes, while V_(m) denotes the voltage across the cell membrane. Nodal analysis provides an equation for the solution of V_(m) : ##EQU1## Rearranging equation 1 to solve for V_(e), we have ##EQU2## The discharge of a single capacitor in such a circuit is well-known, is modeled by

    V.sub.e =e.sup.(-t/R.sbsp.s.sup.C.sbsp.s.sup.),

and so may be placed into equation 2 to give: ##EQU3## where τ_(m) =R_(m) C_(m) represents the time constant of the myocardial cell in the circuit model, and τ_(s) =R_(s) C_(s) represents the time constant of the defibrillator shock in the circuit model. This differential equation models the effects of a monophasic, time-truncated, capacitor-discharge defibrillator on the myocardium.

Equation 3 is a first-order linear differential equation, and may be written as ##EQU4## In the form of equation 4, the general solution is ##EQU5## where c is an integration constant. Integrating equation 5 and simplifying the resultant expression, we have for the membrane voltage at the end of the first phase: ##EQU6## To determine the constant of integration c, we assume the initial value for V_(m) to be V_(m1) (0)=0. Applying the initial condition to equation 6, we have ##EQU7## Therefore, the solution to our initial-value problem for phase 1 is ##EQU8##

A biphasic waveform reverses the flow of current through the myocardium during the second phase. The simplified model of FIG. 4 may again be used by merely reversing the flow of current in the circuit model by changing the sign on the shock current. We thus derive an almost identical differential equation to equation 3 above. The difference is the sign on the right hand side: ##EQU9##

At the beginning of phase 1, we assumed a normalized value of 1 for the charge found on the capacitor at the time the defibrillation shock was initiated, so that equation 3 may be more explicitly written as ##EQU10## At the beginning of phase 2, the capacitor has discharged for a period of time equal to the length of phase 1, and we shall denote this time period as d₁ (the duration of phase 1). The normalized capacitor charge at the start of phase 2 is therefore e^(-d1/)τd <1, and so equation 8 may be written more explicitly as ##EQU11##

Equation 9 is again a first-order linear differential equation, and we write this equation in the form below to apply standard methods for determining its solution: ##EQU12## In the form of equation 10, the general solution is ##EQU13## To determine the constant of integration c, we note that at the end of phase 1 the (initial) value for Vm₂ is ##EQU14## Applying the initial condition to equation 11, we have ##EQU15## Therefore, the solution to the initial-value problem for phase 2 is ##EQU16## which may be rewritten as: ##EQU17##

The requirement defining an optimal pulse duration for phase 2 is that the phase 2 pulse leave as little residual membrane potential remaining on a non-depolarized cell as possible. Equation 12 provides a means to calculate the residual membrane potential at the end of the second phase for those cells that did not depolarize. To determine the optimal phase 2 pulse duration, we set equation 12 equal to zero and solve for t. This optimal pulse duration for phase 2, then, is d₂. To begin, we have ##EQU18## Because (τ_(s) /(τ_(s) -τ_(s))) cannot be zero, we solve for t using the equation

    0=K.sub.m e.sup.-t/τ.sbsp.m -K.sub.s e.sup.-t/τ.sbsp.s.

Arranging the exponential functions onto the left hand side, we get ##EQU19## Taking the logarithm of each side, solving for t, and rearranging terms, we get ##EQU20##

For typical values of a 140 μF capacitor and a 50 Ω electrode resistance the time constant (τ_(s)) will be 7 ms. Assume that τ_(m) is the membrane time constant. The durations of the two phases will be referred to as d₁ and d₂ respectively. The membrane potential at the end of phase one will be given by Equation 7 as

    V.sub.m1 =(τ.sub.s /(τ.sub.s -τ.sub.m)) (e.sup.-d1/τs -e.sup.-d1/τm)

The subtraction of the two exponentials represents the attempt by the discharge capacitor of the ICD (as represented by the positive term with time constant τ_(s)) to charge the membrane while the membrane capacitance is resisting the charging with its electrical inertia (as represented by the negative term containing τ_(m)).

The membrane voltage at the end of the second phase is given as the following equation rearranged from Equation 12:

    V.sub.m2 =(τ.sub.s /(τ.sub.s -τ.sub.m)) (2e.sup.-d1/τs -e.sup.-d1/τm)e.sup.-d2/τm -e.sup.-d1/τs e.sup.d2/τ !

This intimidating equation is necessary to reflect the interaction between the two phase durations and two the time constants.

The fundamental hypothesis of the model of the present invention is that a low residual membrane voltage lowers the electrical requirements of the first phase. This presents an interesting teleological question. How can the second phase affect the first phase when the first phase precedes it? More anthropomorphically, the first phase doesn't even know that the second phase is coming. The answer is as follows: The lower residual membrane voltage (as a result of the second phase of the shock) reduces the necessary current (of phase one) that would otherwise be required to extinguish the additional local arrhythmias caused by the higher residual membrane voltage.

The electrical content of the first phase could be represented in many fashions. To correct for varied durations, the "effective" current model is used as set forth in U.S. Pat. No. 5,405,363 entitled IMPLANTABLE CARDIOVERTER DEFIBRILLATOR HAVING A SMALLER DISPLACEMENT VOLUME. The effective current is simply the average current divided by the "duration correction". The effective current is also equal to the rheobase current for shocks exactly at the threshold level. The function of the duration correction is to normalize the average current for the higher requirements of narrower pulses which is given by the strength duration curve.

The duration correction is:

    1+(d.sub.c /d)

and thus the effective current is given by:

    I.sub.eff =I.sub.ave / 1+(d.sub.c /d)!

The model of the present invention predicts that the required effective current has a minimum value which will be referred to as I_(o) for a perfectly shaped biphasic wave leaving a zero residual membrane potential. The model then further predicts that the increase in required effective current from this I_(o) value is proportional to the excess membrane potential squared. In other words:

    I.sub.eff =I.sub.o +kV.sub.m.sup.2

Application of the New Model

To begin with, the new model will be applied to the known characteristics and experimental results of biphasic waveforms to see whether the model accurately predicts these.

Model Agreement with Reduction in Post Shock Arrhythmias--This new model does not purport to explain all of the findings of reduced post shock arrhythmias. A fundamental tenet of the model, however, is that the increased efficacy of the biphasic waveform is due to reduction in these arrhythmias. Thus, it is axiomatic that this finding is congruent with the model as it is on of the primary hypotheses of the model.

Explanation of the Minimal Benefit of the Symmetrical Waveform--As observed earlier, biphasic waveforms with symmetrical phases have been shown to offer minimal or no benefit--certainly for defibrillation thresholds in terms of energy (as opposed to a square-wave voltage). An analysis of FIG. 5 explains why this result might be seen in the animal model and in this quantitative model. To approximate a symmetrical biphasic waveform a large capacitor (2000 μF) and a 50 Ω electrode is assumed. A 5/5 ms biphasic waveform is then produced. Note that the two phases are fairly symmetric. The cell membrane voltage is noted to rise to about 0.75 during the first phase and then fall rapidly during the second phase. Because the current flow is reversed between the phases, the cell membrane is discharged more rapidly during this second phase than it was charged during the first phase. Therefore the cell voltage is "pulled through" zero during the second phase and is left at a high negative potential of about 0.5. This potential is 2/3 as large in magnitude as that which was found at the end of the first phase.

As can be seen, the second phase did not serve to remove residual cell voltage--but rather served primarily to change its polarity. The present model suggests that there is no advantage in having a mere polarity change in the residual cell voltage 19. Thus the symmetric biphasic should have only a minimal advantage over the monophasic waveform for defibrillation thresholds.

Model Explanation for Benefit of a Shorter Second Phase--As previously indicated, several earlier studies have shown that it is important that, at least in a single capacitor biphasic waveform, that the duration of the second phase be less than or equal to the duration of the first phase. The equations given earlier can be solved to show the relationships between the two different phase durations. It can be directly shown, for reasonable electrode resistances and presently used capacitance values in a single capacitor system, that the second duration should be always smaller than the first--for the lowest threshold.

This finding can also be derived directly from the model more intuitively from a review of the membrane and electrode voltages in FIG. 1. Again the basic principal is that the discharge rate in the second phase is greater than the charge rate during the first phase. Therefore if the first phase was equal in amplitude and duration to the second phase the second phase would still leave a large reverse voltage membrane potential 19. This is true even for the unequal phase voltages seen with practical capacitor sizes.

Consider for example the 150 μF capacitor used for the example in FIG. 1. Even though the capacitor is discharging at a sufficient rate so that the electrode voltage in the second phase is significantly lower than that of the first phase, the membrane discharge rate is still significantly greater in phase two. The membrane capacitance was charged for 3.5 ms during the first phase. A close inspection in FIG. 1 shows that the membrane capacitance would be fully discharged in a little over 2 ms of the second phase. If the second phase was equal in duration to the first phase (i.e. total duration=7 ms) then the membrane potential would be seen to be negative and thus non optimal. However, that negative potential would still be closer to zero than that which would have occurred with no second phase (i.e. with a 3.5 ms monophasic waveform). For this reason single capacitor waveforms in which both phases are equal still offer benefits over the monophasic waveforms. Nevertheless, they are not the optimal biphasic waveform for presently used capacitor values. As taught by the present invention, however, this is not true for smaller, and possibly more optimal, values of capacitances, as well as for disparate dual capacitor systems.

Model Explanation for the Reduced Transthoracic Advantage--Transthoracic defibrillation may produce a more symmetrical distribution of current and potential gradients in the heart than is found with epicardial defibrillation. This would imply that the ratio of minimum to maximum fields is much lower with transthoracic defibrillation that it is with epicardial defibrillation. Therefore, with a shock of sufficient strength to synchronize the overwhelming majority of the heart, there is a much lower likelihood of a substantial mass of cells being partially stimulated and with pro-arrhythmic residual charges. Thus, the "burping" action of the second phase would act on a much smaller population of cells for the transthoracic case than it would for the epicardial defibrillation case. This would reduce the benefit of the second phase and hence of the biphasic wave itself.

Deleterious Effects of the Residual Charge--The residual charge may interfere with defibrillation at two extremes. In the first case the excessive field will leave a charge on the membrane which is intrinsically harmful and proarrhythmic. In the second case a borderline stimulation field will fail to assertively capture and hence synchronize the cell. For both of these cases an implicit hypothesis of the model of this invention is that (at least some) of the deleterious effects of the shock are prevented or minimized by immediately removing the residual charge left by the shock.

Direct experimental data supporting this hypothesis is limited. It is accepted that repolarizing current pulses will reduce the incidence of early after depolarizations. January C T, Shorofsky S., "Early After depolarizations: Newer Insights into Cellular Mechanisms", J Cardiovascular Electrophysiology 1990;1:161-169. Indirect evidence in favor of the second effect (borderline stimulation) was found in studies that showed that the first reactivation, following an unsuccessful monophasic shock, is in the area that had received the smallest electrical field. Shibata N, Chen P S, Dixon E G, et. al., "Epicardial Activation After Unsuccessful Defibrillation Shocks in Dogs", American J Physiology 1988;255:H902-H909; Chen P S, Shibata N, Dixon E G. "Activation During Ventricular Defibrillation in Open-Chest Dogs", J Clinical Investigation 1986;77:810-823. Despite these results, the authors of these two studies concluded, "These findings suggested that the shock extinguished all of the activation fronts present during fibrillation, but, after a latency period, the shock itself gave rise to new activation fronts that caused fibrillation to be reinitiated." This conclusion is inapposite to the model of the present invention which concludes that it is the excess charge on the cell membranes, and not the shock itself, that would give rise to new activation fronts that would cause post shock arrhythmias.

Effects of Borderline Fields--As previously indicated, one of the possible consequences of the model of the present invention is an explanation of the borderline field phenomenon. Using the Hodgkin-Huxley model of invitro cell propagation that, when the local response has almost reached propagating size, it becomes unstable and varies from shock to shock, computer estimates of stimulation strength-duration curves have shown that ". . . a highly unstable subthreshold propagating wave is initiated in principle by a just threshold stimulus." Cooley J W, Dodge F A., "Digital Computer Solutions for Excitation and Propagation of the Nerve Impulse", Biophysical Journal 1966;6:583-599. Four different cellular models have also been studied with borderline strength stimulation, and all four models showed similar activation delays possible of 20, 12, ">20," and 8 ms respectively. Krassowska W, Cabo C, Knisley S B, et.al., "Propagation vs. Delayed Activation During Field Stimulation of Cardiac Muscle", PACE 1992;15:197-210. Latencies and other graded responses also have been experimentally observed in mammalian cardiac tissue. Kao C Y, Hoffman B F, "Graded and Decremental Response in Heart Muscle Fiber",American j Physiology 1958;194 (1):187-196.

The above results suggest an intriguing possibility extending from the present model. When the shock is delivered to the heart, at threshold, there are regions of the heart that will receive an insufficient field for countershock stimulation. In the transition zone between these non-stimulated cells and the stimulated cells, there will be cells that will receive a borderline stimulation of the type which has been analyzed by this model. These borderline stimulated cells would then be activated with a significant delay or an unstable response. This could be sufficient to destroy the synchronization desired from the defibrillation shock. The second phase of the defibrillation shock, by removing that residual charge, may be able to arrest the delayed and unstable responses. This would then eliminate this source of desynchronization.

Application of the New Model to Existing ICD Systems

Presently available ICD systems offer, in some cases, programmable tilts and durations. It is important to know the optimal values of these programmable parameters. According to the present model, these parameters are functions of 4 variables: the electrode resistance, the ICD capacitance, the chronaxie time, and the membrane time constant. The calculated values are fairly insensitive to changes in the chronaxie time and membrane time constant. The primary sensitivity is to the electrode resistance and ICD capacitance.

The ICD capacitance in present devices ranges from 85-180 μF. The electrode resistance varies from 25 Ω to 100 Ω depending upon the electrode system. In addition, the electrode impedance can vary over a 2:1 ratio from the time of implant to a 1 year follow-up. Schwartzman D, Jadonath R, Estapo J, et.al., "Serial Patch--Patch Impedance Values in an Epicardial Defibrillation System", PACE 1993;16:916 (Abstract).

Optimal phase durations for single capacitor systems--Calculations are simplified by the fact that the value of the electrode resistance and ICD capacitance are combined in the simple electrical time constant of τ_(s) =RC. As taught by U.S. Pat. No. 5,405,363 entitled IMPLANTABLE CARDIOVERTER DEFIBRILLATOR HAVING A SMALLER DISPLACEMENT VOLUME, the first phase duration is given by that of the optimal monophasic pulse.

    d.sub.1 =0.58τ.sub.s +0.58d.sub.c

where τ_(s) =RC is the shock time constant and d_(c) is the chronaxie duration. This formula codifies the necessary compromise between the electronics (having a sufficient duration to discharge the capacitor) and the heart (having a duration near the chronaxie time).

The equation giving the residual membrane voltage, for the end of phase 2, may be solved for the duration which restores the potential to a zero voltage (actually a zero departure from initial). The optimal value of the second phase duration is given by Equation 16:

    d.sub.2 (opt)= (τ.sub.s τ.sub.m)/(τ.sub.s -τ.sub.m)!ln 2-(e.sup.-d.sbsp.1.sup./ τm/e.sup.-d.sbsp.1.sup./ τs)!

The optimal durations for a single capacitor system are shown in FIG. 6. A chronaxie duration of 2.4 ms is assumed for phase one which is given by the top curve. The lower curve is the optimal phase two duration which is given by the d₂ equation above. Note that the phase one duration increases linearly with the time constant. Note that the phase two duration decreases initially and is essentially constant for increasing RC time constants. The phase 2 duration of 2.5 ms appears to be a reasonably accurate value regardless of the RC time constant (at least for present values of R and C).

At first it may seem counter-intuitive that the optimum phase two duration is essentially constant regardless of the RC time constant--especially while the phase one durations are changing. However, for a large RC time constant, there will be an increasing voltage remaining on the capacitor for use in the second phase. Thus a second phase will have a large discharge capability. At the same time, for the optimal first phase duration, the cell membrane voltage will be increased. These two factors tend to work in balance. In other words, there is a greater membrane charge to be discharged, but there is a greater capacitor charge and hence a greater discharge capability to be applied to the membrane.

Conversely, for the case of a smaller RC time constant (in the range of 4-6 ms) the capacitor is more discharged at the end of the first phase. Thus there is less discharge capability in the second phase of the biphasic wave. However this is balanced out by the fact that the cell membrane had less time to charge up and thus there is less to discharge from the cell membrane itself. These intuitive arguments, and the quantitative results from the model run counter to some standard practice, which is to make the second phase duration proportional to that of the first phase.

FIG. 7 shows how the optimal phase 2 duration for a single capacitor system varies as a percentage of that of phase one. It is seen that there is no constant relationship. The phase two duration, for an optimal biphasic wave, is 186% of the phase one duration for a τ₁ =RC=2 ms and falls steadily to only 21% of the phase one duration for τ₁ =18 ms.

Optimal tilts for each phase of a single capacitor system--Some existing ICD systems have durations specified as a "tilt". As can be seen in FIG. 8 the optimal tilt is reasonably constant for phase one regardless of the RC time constant. It varies between 50-65% for reasonable values. Thus its use is defensible. However, the phase two optimum tilt varies from 65% down to only 13% for a reasonable range of time constants. Thus the use of a tilt specification for the second phase of a biphasic waveform is probably not defensible. It is also probably not advisable to use a phase two duration which is defined as a percentage of the phase one duration (when that phase one duration itself is tilt defined).

Optimal capacitance for a single capacitor system--As taught by U.S. Pat. No. 5,405,363 entitled IMPLANTABLE CARDIOVERTER DEFIBRILLATOR HAVING A SMALLER DISPLACEMENT VOLUME, the capacitance value of the capacitor system has a significant impact on defibrillation thresholds. The present biphasic model implicitly assumes that the optimum first phase of the biphasic waveform should be the same as the optimal monophasic waveform, because the function of the second phase is not to stimulate, but only to "burp" the residual charge. The monophasic modeling set forth in the above identified application suggests that the optimum capacitance is given by choosing it such that:

    τ.sub.s =RC=0.8d.sub.c.

This gives a pulse width tuned to the chronaxie time and minimizes the stored energy requirements. The stored energy requirement determines the size of the ICD system and thus is critically important. For an assumed chronaxie time of 2.7 ms this suggests that:

    τ.sub.s =RC=2.16ms

For a typical electrode impedance of 50 Ω one would have an optimal capacitance value of C=43.2 μF. The optimal pulse duration given by the earlier equation for phase one (or for the monophasic wave) would be 2.82 ms. The solution of the biphasic equations gives an optimal duration for phase two of about 6 ms. This suggests a phase two duration in excess of the phase one duration. While this is contrary to the reported results that phase 2 should be shorter than phase 1 for single capacitor systems, all of these results presumed capacitance values of greater than 140 μF. In addition, because the tilt for the optimum second phase would be over 95% (and not 100%), the single capacitor system, while nearly exhausted during the second phase, would still have some residual charge to meet the goal of discharging the membrane capacitance.

Application of the Model to Disparate Dual Capacitor Systems

FIG. 9 shows a simplified schematic of the circuitry 60 that is used to produce the disparate dual capacitor biphasic waveform 100 as shown in FIG. 10. Battery system 62 activates a primary winding on flyback split winding transformer 64 when switch 66 is activated at a high frequency by controller 68. Each of the split secondary windings 64a and 64b of transformer 64 charges a separate capacitor system 70 and 72, through diodes 74 or 76, respectively. It will be apparent from the configuration of diodes 74 and 76 that capacitor systems 70 and 72 are charged to opposite polarities.

One of the key advantages of the disparate dual capacitor embodiment of the present invention is the elimination of the conventional H-bridge switch arrangement as shown in FIG. 2. In FIG. 9, however, only two switches are required to deliver the biphasic waveform 100, switches 77 and 78, which may be of various types and are not limited to the SCR type of switches that are presently required to implement the conventional H-bridge switch arrangement. During delivery of first phase 102 (FIG. 10), switch 77 is closed and switches 78 is open. At the transition point at the end of first phase 102 and the beginning of second phase 104, controller 68 opens switch 77 stopping the discharge from capacitor system 70, and closes switch 78 to discharge capacitor system 72 to electrodes 80 and 82, thereby producing biphasic waveform 100. Circuitry 70 is significantly simpler than circuitry 20 of FIG. 2 and does not have the inherent unreliability problems. Circuitry 70 also allows for the use of a smaller capacitance for capacitor system 70 as it does not need to store additional charge for the second phase of the biphasic waveform 100. While the capacitor systems 70 and 72 are shown as single capacitors, it will be recognized that two or more individual capacitors can be used for each capacitor system, so as to achieve the desired charging voltages of effective capacitance value, for example.

For the biphasic waveform 100 as shown in FIG. 10, capacitor system 70 is 60 μF and capacitor system 72 is only 10 μF; however, capacitor system 72 is charged to the same voltage, but with the opposite polarity, as capacitor system 70. In this example, the second phase voltage returns to 0 relative voltage at a very rapid rate. This is due to the small time constant of capacitor system 72, which in this case is only 0.5 ms. Consequently, in this embodiment, capacitor system 72 is discharged before the cell membrane voltage is discharged and the goal of the present model for biphasic waveforms is not achieved. The basic problem with this particular embodiment is that the cell membrane is thought to have a time constant on the order of about 3 ms. Thus, any capacitor system 72 generating the second phase of the biphasic waveform should have an effective time constant of greater than about 3 ms, otherwise the capacitor system will be discharged before the cell membrane is discharged.

FIGS. 11-15 explore the performance of various charging voltages and capacitance values combinations for capacitor system 72 which provide a consistent initial charge for capacitor system 72, and therefore require similar charging energies, in order to determine an optimum arrangement for capacitor system 72. In all of these examples, capacitor system 70 has an effective capacitance of 60 μF and an initial charging voltage of 750 volts, for example, (achieved by the series combination of two electrolytic capacitors each having a capacitance value of 120 μF), in order to provide a total stored energy for capacitor system 70 of 16.9 joules.

Capacitor system 72, on the other hand, is chosen in all of the examples, except for FIG. 14, so as to provide a total stored energy of less than one joule. Because the stored energy of a capacitor system effectively determines the overall size of the capacitor system, it can be seen that for each of these examples, the overall size of capacitor system 72 is less than 10% of the size of capacitor system 70. It will further be recognized that it is this disparate stored energy capacity which distinguishes capacitor system 70 from capacitor system 72 and gives rise to the various advantages of this embodiment of the present invention.

Referring now to FIG. 11, another biphasic waveform 110 is shown. In this example, capacitor system 72 has a capacitance value of 50 μF, but an initial charging voltage of only 20% of capacitor system 70. In this case, the stored energy of capacitor system 72 is only about 0.6 joules. Note that the discharge time constant of the second phase is approximately equal to that of the first phase due to the relatively small difference in effective capacitances between capacitor system 70 and capacitor system 72. In this example, capacitor system 72 is capable of discharging the cell membrane by about 9 ms after the beginning of the countershock, a time period which, according to the biphasic model of the present invention, should be sufficient to capture all of the benefits of the second phase of the biphasic waveform.

In FIG. 12, the effects of using a high capacitance value (100 μF) and lower charging voltage (14% of the maximum charging voltage) for capacitor system 72 are shown. Again, capacitor system 72 stores less than 5% of the energy of capacitor system 70. In this example, however, the cell membrane is predicted to be discharged to 0 at about 8 ms from the start of the countershock. This would suggest possibly a slight improvement over the combination as shown in FIG. 11.

In FIG. 13, the same stored energy is used again, only a still higher capacitance value (200 μF) and a still lower charging voltage (10% of the maximum charging voltage) are used. It is again seen that capacitor system 72 is able to discharge the cell membrane in about 8 ms. This would suggest no apparent improvement over the combination shown in FIG. 12.

FIG. 14 shows the influence of using a higher voltage for capacitor system 72. As with FIG. 13, a higher capacitance value (200 μF) is used, only in this example the voltage is increased (to 20% of the maximum charging voltage). This increases the stored energy requirements for capacitor system 72 to approximately 2.25 joules, meaning that the size would be more than doubled as compared to capacitor system 72 for FIGS. 11-13. Note that the benefit of increasing the charging voltage in FIG. 14 is that the cell membrane voltage is restored to 0 at about 6.5 ms. This probably does not represent any real advantages as recent research has suggested that the biphasic waveform maintains its efficacy benefit even when the two phases are separated by several milliseconds. Cooper R, Wallenius S T, Smith W M, Ideker R E, "The Effect of Phase Separation on Biphasic Waveform Defibrillation", PACE, Vol. 6, March, Part I, 1993. When combined with the new model for biphasic waveforms of the present invention, this research suggests that the important restoration of the cell membrane voltage to 0 need not occur instantaneously, but that perhaps it is sufficient if the cell restoration to 0 occurs within 6 to 10 ms from the start of the second phase.

In FIG. 15, the stored energy of capacitor system 72 is returned to the subjoule level. In this example, the capacitance value is selected at 400 μF and the charging voltage is only about 7% of the maximum charging voltage. Note that for this combination, the cell membrane potential is restored to 0 at about 9 ms. Thus, there appears to be little sensitivity to the trade off between capacitance value and voltage value for a fixed energy level in the second phase. It may also be seen that an extremely low level of energy is all that is necessary in the second phase to obtain the benefits of the biphasic waveform in accordance with the model used by the present invention.

FIG. 16 demonstrates another disparate dual capacitor approach. As previously indicated, the analysis of effective current set forth in U.S. Pat. No. 5,405,363 entitled IMPLANTABLE CARDIOVERTER DEFIBRILLATOR HAVING A SMALLER DISPLACEMENT VOLUME suggests that the optimum capacitance value for capacitor system 70 would be on the order of 40 μF. FIG. 16 plots a single capacitor biphasic using a 40 μF capacitor. Here, a first phase pulse of 3 ms is shown and it appears that the second phase could discharge the cell membrane to 0 potential at about 9 ms

This predicted discharge is misleading, however, because the discharge curve in FIG. 16 is based on the cell membrane discharging with a time constant of 3 ms through the current offered through electrodes 42 and 44, for example. Unfortunately, the output of the cardiac electrodes 42 and 44 is very nonlinear. In particular, cardiac electrodes 42 and 44 have a very high resistance for voltages below about 20 volts. This is due to the nonlinear interactions of the electronic current in the electrode metals and the ionic currents in the heart, as well as nonlinearities in the impedance of the heart muscle itself. In this example, the actual capacitor voltage at the end of 9 ms would be about 3.8 volts. Thus, the electrodes 42 and 44 would not be "turned-on" and the discharge characteristics shown in FIG. 16 would probably not occur at the cell membrane level. As a note, the final discharge voltage of FIG. 13, for example, would be about 33 volts, which should be sufficient to keep the electrodes "turned-on" and thereby obtain the intended benefits of the second phase of the biphasic waveform.

FIG. 17 is a waveform for a disparate capacitor system of the type shown in FIG. 9 wherein capacitor system 70 is 40 μF and capacitor system 72 is 100 μF, but charged to only 12% of the maximum charging voltage of capacitor system 70. FIG. 18 shows a similar arrangement to FIG. 17, only the charging voltage for capacitor system 72 is increased. As a result, the cell membrane potential is restored in about 6.5 ms, as compared to 9 ms for FIG. 17. The disadvantage is that capacitor system 72 would be almost twice as large for the arrangement of FIG. 18.

FIG. 19 shows an alternative embodiment of the circuitry 160 for the disparate dual capacitor system of the present invention. The battery, primary transformer and switching circuitry are similar to FIG. 9 and are not shown for ease of representation. In this embodiment, the transformer has a secondary windings 164 which charge a capacitor 170 through diode 174. In this example, capacitor system 170 has a capacitance of 85 μF. The secondary windings 164 also slowly charges capacitor system 172 through diode 176 using the heart 44 as the return path. This has a disadvantage of conducting a small bit of current through the heart during fibrillation; however, this should not damage the heart and there is no concern over electrically disturbing the heart as it is in fibrillation anyway. Switch 178 is used to discharge capacitor system 170 through the heart 44 to form the first phase of the biphasic waveform. At the end of the first phase, switch 179 is turned on which conducts capacitor system 172 in a reverse fashion to the heart to generate the second phase.

The advantage of this embodiment is that no additional secondary winding is required for the transformer. The disadvantage is the capacitor system 172 is charged to the full voltage of capacitor system 170. To maintain a low energy requirement for capacitor system 172, its capacitance value will need to be small, in this example on the order of 10 μF, which may lead to the efficacy problems discussed with respect to FIG. 10.

FIG. 20 represents another alternate embodiment of the disparate dual capacitor system of the present invention. In this example, the two capacitors 270a and 270b are a pair of electrolytic capacitors charged in series by secondary windings 264a and 264b through diode 274a and 274b, respectively, to function as one capacitor system 270 during the first phase. The charging of capacitor system 272 is similar to FIG. 19, however, capacitor system 272 is only charged to one-half of the maximum charging voltage by locating at the midpoint between capacitors 270a and 270b.

A further alternate embodiment of the disparate dual capacitor system of the present invention is shown in FIG. 21. Here, transformer 364 has two secondary windings 364a and 364b. Winding 364a charges capacitor system 370 through diode 374 and winding 364b charges capacitor system 372 through diode 376 to a negative voltage. For the first phase, SCR 380 is turned on by controller 368 and delivers current in a forward direction to the heart. At the end of the first phase, SCR 382 is turned on. This rapidly discharges capacitor system 370 through a low level resistance 384. Resistance 384 has a small value and is designed merely to protect switch S2 and circuitry paths from excessive currents during the rapid discharge of capacitor system 370. This serves to truncate the first phase of the biphasic waveform. After this is completed, controller 368 enables SCR 386. This delivers the negative voltage of capacitor system 372 to the heart, thereby providing phase two. At the appropriate truncation time for phase two, SCR 380 is turned on again. This results in the rapid discharge of capacitor system 372, finally terminating the second phase of the biphasic waveform.

A still further alternate embodiment of the disparate dual capacitor system of the present invention is shown in FIG. 22. In this embodiment, the residual charge on capacitor system 470 is shorted to capacitor system 472 to provide the energy for the second phase of the biphasic waveform. As with the other embodiments, controller 468 operates transformer winding 464 to charge capacitor system 470 through diode 474. To generate the first phase of the biphasic waveform, switch 480 is turned on. At the end of the first phase, switch 482 is turned on to short the remaining charge on capacitor system 470 to capacitor system 472. Switch 484 is then turned on to back bias and turn off switch 480. Switch 486 is then turned on to deliver the charge in capacitor system 472 to the heart as the reverse current for the second phase of the biphasic waveform.

The advantage of this embodiment is that it avoids another secondary winding on the transformer and make use of the energy that would otherwise be wasted in capacitor system 470 when the first phase is truncated. The values of capacitor system 470 and 472 need to be selected such that there is at least twice the stored energy remaining in capacitor system 470 at the time the first phase is truncated to transfer to capacitor system 472 in order to compensate for transfer inefficiencies of up to 50%. In addition, the capacitance value and initial charging voltages of capacitor system 472 need to be selected to deliver a second phase that is longer than 3 ms and has a final truncation voltage of above about 20 to 30 volts. For capacitor systems 472 equal to 100 μF and a truncation voltage at the end of phase one of 250 volts (producing a 50% transferred voltage of 125 volts), capacitor system 472 could store about 0.75 joules and deliver a 5 ms pulse having a final voltage of about 48 volts. To accommodate this transfer, capacitor system 470 would have to retain about 1.5 joules at the time the first phase was truncated, something which is quite feasible if the capacitance value is greater than about 50 μF. 

We claim:
 1. An improved implantable defibrillator system for producing a biphasic capacitive-discharge countershock to be delivered to a human patient, the implantable defibrillator system including at least two implantable electrodes and a self-contained human implantable housing containing a waveform-generating capacitor means for storing an electrical charge, means for charging the waveform-generating capacitor means, means for sensing of a myocardial dysrhythmia in the human patient and means for selectively discharging the electrical charge in the waveform-generating capacitor means as a countershock to be delivered through the at least two implantable electrodes in response to the means for sensing of the myocardial dysrhythmia in the human patient, the improvement comprising:the waveform-generating capacitor means including at least two disparate capacitor systems, a first capacitor system for storing a first electrical charge used to generate a first phase of the biphasic countershock, and a second capacitor system for storing a second electrical charge used to generate a second phase of the biphasic countershock, the second electrical charge being stored separate and distinct from the first electrical charge, being of less energy than the first electrical charge, and being discharged at a discharge time constant that is less than a discharge time constant for the discharge of the first electrical charge.
 2. The defibrillator system of claim 1 wherein the second capacitor system has an effective capacitance different than an effective capacitance of the first capacitor system.
 3. The defibrillator system of claim 1 wherein the second capacitor system has an effective capacitance that is higher than an effective capacitance of the first capacitor system and a charging voltage that is lower than a charging voltage of the first capacitor system.
 4. The defibrillator system of claim 1 wherein the first capacitor system has a rated charging voltage of at least about 700 volts and an effective capacitance of between about 20 and 100 μF, and the second capacitor system has a rated charging voltage of less than about 250 volts and an effective capacitance of greater than about 50 μF.
 5. An implantable defibrillator apparatus for treating myocardial arrhythmias in a human patient by delivering a biphasic countershock comprising:at least two implantable discharge electrodes; sensing means for sensing a myocardial arrhythmia in the human patient; a first capacitor means for storing a first electrical charge; a second capacitor means for storing a second electrical charge that is separate from and less than the first electrical charge and that will discharge at a discharge time constant that is less than a discharge time constant of the first capacitor means; power source means for charging the first and second capacitor means to a first and second charging voltage; and control means for selectively controlling the power source means and the capacitive charge storage means in response to the sensing of the myocardial arrhythmia in order to deliver a biphasic countershock to the at least two implantable electrodes by delivering a first phase of the biphasic countershock from the first electrical charge stored in the first capacitor means, and by delivering a second phase of the biphasic countershock from the second electrical charge stored in the second capacitor means.
 6. The defibrillator apparatus of claim 5 wherein the second capacitor means has an effective capacitance different than an effective capacitance of the first capacitor means.
 7. The defibrillator apparatus of claim 6 wherein the second capacitor means has an effective capacitance that is higher than an effective capacitance of the first capacitor means and a charging voltage that is lower than a charging voltage of the first capacitor means.
 8. The defibrillator apparatus of claim 5 wherein the first charging voltage is higher than the second charging voltage.
 9. The defibrillator apparatus of claim 5 wherein the first capacitor means has a rated charging voltage of at least 700 volts and an effective capacitance of between 20 and 100 μF, and the second capacitor means has a rated charging voltage of less than 250 volts and an effective capacitance of greater than 50 μF.
 10. The defibrillator apparatus of claim 5 wherein the first capacitor means is comprised of a pair of electrolytic capacitors connected in series.
 11. The defibrillator apparatus of claim 5 wherein the second capacitor means is comprised of a single capacitor.
 12. The defibrillator apparatus of claim 5 wherein the power source means includes a transformer having at least two separate windings, the transformer being operably connected to the first and second capacitor means and wherein the power source means simultaneously charges the first and second capacitor means through the at least two separate windings of the transformer. 